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A straight line has the equation $y = 2x - 1$ - OCR - GCSE Maths - Question 21 - 2021 - Paper 3

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Question 21

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A straight line has the equation $y = 2x - 1$. Write down the gradient of the line. Here are the equations of four straight lines. $y = 2x + 3$ $y = 1 - x$ $y... show full transcript

Worked Solution & Example Answer:A straight line has the equation $y = 2x - 1$ - OCR - GCSE Maths - Question 21 - 2021 - Paper 3

Step 1

Write down the gradient of the line.

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Answer

The gradient of the line y=2x−1y = 2x - 1 is the coefficient of xx, which is 22.

Step 2

Which of the four straight lines is parallel to $y = 2x - 1$?

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Answer

The line that is parallel to y=2x−1y = 2x - 1 must have the same gradient. Therefore, the line y=2x+3y = 2x + 3 is parallel to it, as both have a gradient of 22.

Step 3

Explain why the student is wrong.

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Answer

The steepness of a straight line is determined by its gradient, not the constant term added. The gradient of the line y=12x+4y = \frac{1}{2}x + 4 is 12\frac{1}{2}, which is less steep than the gradient of 22 from y=2x−1y = 2x - 1. Hence, y=12x+4y = \frac{1}{2}x + 4 is not the steepest line, despite having a larger constant.

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